DOI: 10.3303/CET25120050 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 10 May 2025; Revised: 11 August 2025; Accepted: 7 September 2025 
Please cite this article as: Lugo-Granados H.G., Canizalez Dávalos L., Picón-Núñez M., 2025, The Effect of Fluid Velocity on the Performance 
of Evacuated Solar Thermal Collectors Under Scaling Conditions, Chemical Engineering Transactions, 120, 295-300  
DOI:10.3303/CET25120050 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 120, 2025 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Bing Shen How, Viknesh Andiappan, Denny K.S. Ng, Hon Loong Lam, Petar S. Varbanov 

Copyright © 2025, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-21-2; ISSN 2283-9216 

The Effect of Fluid Velocity on the Performance of Evacuated 

Solar Thermal Collectors Under Scaling Conditions  

Hebert G. Lugo-Granadosa,*, Lázaro Canizalez-Dávalosa, Martín Picón-Núñezb 

aAutonomous University of Zacatecas, Department of Chemical Engineering, Zacatecas, México 
bUniversity of Guanajuato, Department of Chemical Engineering, Guanajuato, Gto., Mexico  

 lugh871024@gmail.com 

The performance of solar collector networks decreases due to scaling fouling caused by the accumulation of 

calcium carbonate (CaCO₃), which reduces thermal efficiency and increases the system pressure drop. This 

study analyses the impact of flow velocity on the outlet temperature and pressure drop in evacuated flat-plate 

solar collectors across different operating times. The results indicate that, with a flow velocity of 4 m/s, scaling 

fouling increases the number of collectors required to reach the target temperature by 12 %. In contrast, with a 

velocity of 0.15 m/s, the collectors increase by 5 %. Operating at higher flow velocities helps mitigate fouling, 

resulting in a minor reduction in the outlet temperature. On the other hand, lower flow velocities promote the 

accumulation of deposits and accelerate the loss of thermal efficiency. The analysis found that the pressure 

drop increases due to three main factors: fouling caused by scaling, the installation of collectors in series, 

especially when exceeding ten collectors and extended operating periods of the solar network (t > 2,160 h). The 

results showed that it is necessary to improve flow distribution to ensure good performance and extend the 

lifespan of solar collector networks under fouling conditions. 

1. Introduction 

Evacuated flat-plate solar collectors represent an efficient solution for harnessing solar thermal energy in various 

applications, especially in industrial processes requiring medium temperatures between 120 and 180 °C (Gao 

et al., 2020). Evacuated flat-plate collectors (EFPC) combine the design of traditional flat-plate collectors (FPC) 

with the vacuum principle of evacuated tube collectors (ETC). The collector vacuum system minimises 

convective heat losses, enhancing thermal efficiency and reducing space requirements compared to ETCS 

(Carrión-Chamba et al., 2022). However, their performance can be affected by the accumulation of mineral 

deposits (CaCO₃). This phenomenon, known as scaling, reduces thermal efficiency and increases the system's 

hydraulic resistance, negatively impacting its long-term performance. 

Several numerical studies have evaluated the thermal performance of different types of thermal solar collectors. 

Albizzati (2016) conducted a comparative analysis between flat-plate collectors (FPC) and evacuated tube 

collectors (ETC). This study demonstrated that FPCs exhibit lower thermal efficiency (34 %), while ETCs achieve 

values from 46.3%. Bellos et al. (2023) analyzed an EFPC operating below 200 °C and developed a correlation 

to estimate daily useful energy output based on operating temperature, solar irradiation, and ambient 

temperature. They found that the optimal exergy and thermal efficiencies were 13.33 % and 47.24 % at 125 °C, 

with energy and exergy costs of €0.0274/kWh and €0.1043/kWh. In parallel, computational studies have focused 

on modeling the thermal and hydraulic behavior of solar collectors. Nedunchezhiyan et al. (2023) employed 

numerical simulations to analyze hybrid evacuated tube and flat plate solar collectors, examining the impact of 

different flow rates on velocity, pressure, temperature, and turbulent kinetic energy. Their findings indicate that 

a flow rate of 1 L/min maximizes thermal efficiency (68.5 %). Additionally, Haghverdi et al. (2023) developed a 

CFD model for a polycarbonate flat plate solar collector, validating their numerical results against experimental 

data, which enabled design optimization and cost analysis. However, these studies do not account for the effects 

of scaling fouling, a limitation that affects their long-term applicability. 

 

295



In recent studies, Lugo-Granados et al. (2023) focused their research on the impacts of scaling fouling on the 

instantaneous thermohydraulic performance of solar collector fields. In a subsequent study, Lugo-Granados et 

al. (2024) determined that the optimal design of a flat-plate solar collector network in continuous operation can 

generate annual savings of $ 17,523 under clean conditions and $ 19,819 under fouling conditions, compared 

to the operational cost of using natural gas. They evaluated various network arrangements to maximize 

production in a batch process, considering the impact of scaling fouling on system performance.  

This study analyses how scaling accumulation can intensify in solar collectors operating at reduced flow 

velocities, especially due to inefficient fluid distribution. It also demonstrates that poor flow distribution not only 

affects the system thermal efficiency but also contributes to increased fouling, negatively impacting the lifespan 

and overall performance of the solar collector. 

2. Methodology 

For the analysis of evacuated flat-plate solar collectors, a thermal model is derived from the one used for 

conventional collectors. These systems have the advantage that the vacuum acts as an excellent thermal 

insulator. This significantly reduces energy losses through convection, improving heat retention and increasing 

the system efficiency. Figure 1 illustrates the components of an evacuated flat-plate collector, which consists of 

an aluminum housing serving as the main structure. Additionally, it includes a glass cover, an absorber plate, 

copper tubes for heat exchange, and a lower plate, which together optimize the capture and transfer of thermal 

energy. 

 

Figure 1: a) Vacuum flat plate collector components, b) Heat transfer resistances within the solar system 

The heat flow absorbed by the collectors Eq(1), denoted as �̇�𝑢 (W), is determined by the heat removal factor 

(FR), the collector area As (m2), solar radiation IG (W/m2), the overall heat loss coefficient Uc (W/(m2 °C)), the 

temperature difference between the absorber plate (Tp-Ta) (°C), and the absorptance (𝛼𝑐) and transmittance 

(𝜏) of the cover. 

�̇�𝑢 = 𝐹𝑅𝐴𝑠[𝐼𝐺(𝜏𝛼𝑐) − 𝑈𝑐(𝑇𝑝 − 𝑇𝑎)] (1) 

Figure 2 illustrates the thermal model representing the relationship between the absorber plate temperature Tpm 

(°C) and the ambient temperature Ta (°C). The overall heat loss coefficient UC (W/(m2 °C)) combines three 

components: the top loss coefficient Us (W/(m2 °C)), the back loss coefficient UP (W/(m2 °C)), and the side loss 

coefficient Ul (W/m2°C), as shown in Eq(2). 

𝑈𝑐 = 𝑈𝑠+𝑈𝑝+𝑈𝑙 (2) 

The top heat loss coefficient (US) is defined as the inverse of the sum of the thermal resistances R1 (m2 °C/W) 

and R2 (m2 °C/W) within the collector as indicated in Eq(3). Thermal resistance R1 (Eq(4)) accounts for heat 

transfer via convection (hcc−a (W/(m2 °C))) and radiation (hrc−a (W/(m2 °C))) between the absorber plate and the 

environment. Resistance R2 (Eq(5)) corresponds to the region between the plate and the cover. 

𝑈𝑠 =
1

𝑅1+𝑅2
 (3) 

𝑅1 =
1

ℎ𝑟𝑐−𝑎 + ℎ𝑐𝑐−𝑎
 (4) 

(a) (b) 

296



𝑅2 =
1

ℎ𝑟𝑝−𝑐
 (5) 

The back loss coefficient (Up) depends on thermal resistances from conduction through the insulation (R3 (m2 

°C/W)) and from combined convection and radiation (R4 (m2 °C/W)) between the backplate and the 

surroundings, Eq(6). (R4) is negligible compared to (R3), (Eq (7)). Here, ks is the thermal conductivity and xs is 

the thickness of the back insulation material. 

𝑈𝑝 =
1

𝑅3+𝑅4
 (6) 

𝑅3 =
𝑘𝑠

𝑥𝑠
 (7) 

The side heat loss coefficient (Ul) is derived considering one-dimensional thermal flux across the perimeter and 

area (Ac) collector, as shown in Eq(8). Where xl is the side insulation thickness, p and h are the perimeter and 

the hight of the collector. 

𝑈𝑙 = (
𝑘𝑠

𝑥𝑙
) ∙  (

𝑝 ℎ

𝐴𝑐
) (8) 

The heat removal factor, Eq(9), is a function of the mass flow rate �̇�𝑓 (kg/s), and the efficiency factor of the 

collector. The term F´ in Eq(10) is a function of the tube spacing S (m), the inner diameter di (m) and outer 

diameter do (m) of the tubes, and the heat transfer resistances from the absorber plate to the working fluid. It 

also includes the resistance arising from convection between the inner tube wall and the working fluid Rh (m2 

°C/W). The resistance due to the tube wall Rt (m2 °C/W) and the fouling layer resistance Rs (m2 °C/W). Cb (m2 

°C/W) is the resistance caused by the tube/plate bond and is described in Eq(11).  

𝐹𝑅,𝜃 =
𝑚𝑓̇ 𝐶𝑝𝑓

𝐴𝑠  𝑈𝑐
[1 − 𝑒

−𝐴𝑠 𝑈𝑐𝐹′
𝑚𝑓̇ 𝐶𝑝𝑓 ] (9) 

𝐹′ =
1/𝑈𝑐,𝜃

𝑆 [
1

𝑈𝑐,𝜃[𝑑0 + 𝐹𝐴,𝜃(𝑆 − 𝑑0)]
+

1
𝐶𝑏,𝜃

+
𝑅ℎ,𝜃

𝜋𝑑𝑠
+

𝑅𝑡,𝜃

𝜋𝑑𝑠
+

𝑅𝑠,𝜃

𝜋𝑑𝑠
]

 
(10) 

𝐶𝑏,𝜃 = 𝑘𝑏𝑊 𝛾⁄  (11) 

where kb (W/(m °C)) is the thermal conductivity of the junction, W (m) is the width, and 𝛾 (m) is the thickness of 

the junction between the plate and the tube. Eq(12) is described by the hydraulic diameter ds (m), and xf (m) is 

the thickness by scaling. 

𝑑𝑠 = 𝑑𝑖 − 2𝑥𝑓 (12) 

Additionally, F´ depends on the thermal efficiency of the metal fin (FA) as given by Eq(13). 

𝐹𝐴 =
𝑇𝑎𝑛ℎ[𝑀𝜃(𝑆 − 𝑑0)/2]

𝑀𝜃(𝑆 − 𝑑0)/2
 (13) 

𝑀𝜃 = √(𝑈𝑐,𝜃 (𝑘𝑝,𝜃)𝛿)⁄  (14) 

The terms kp (W/m °C) and 𝛿 (m) represent the thermal conductivity and plate thickness, and the parameter M 

(m⁻¹), is defined in Eq(14). The fouling thermal resistance, Rs (m2 °C/W), is a function of the mass flux of CaCO₃ 

deposited on the tubes, denoted as �̇�𝑑 (kg/(m2 s)), mass flux being removed, �̇�𝑟 (kg/(m2 s)), the density ρf 

(kg/m3), and the thermal conductivity λf (W/m °C) of CaCO₃, Eq(15). 

𝑑𝑅𝑠,𝜃

𝑑𝑡,𝜃
=

�̇�𝑑,𝜃 − �̇�𝑟,𝜃

𝜌𝑓,𝜃𝜆𝑓,𝜃
 (15) 

To determine the amount of scaling (CaCO₃) deposited on the inner collector tubes, the mathematical model 

developed by Lugo-Granados and Picon-Nuñez (2017) is implemented. Through this model, it is possible to 

understand the effects of scaling fouling on the thermal and hydraulic performance of solar collectors, Eq(16). 

297



�̇�𝑑 =  
𝛽

2
  (

𝛽

𝛼 𝑘𝑟
+ (𝐶1 + 𝐶2) − √

[𝛽 + (𝐶1+𝐶2) 𝛼 𝑘𝑟]2 + 4 𝛼2 𝑘𝑟
2(𝐾𝑠𝑝 − [𝐶1][𝐶2])

𝛼2 𝑘𝑟
2   ) (16) 

The model determines the mass flow rate �̇�𝑑 (kg/m² s) of CaCO₃ deposited on the tubes (scaling formation) 

based on parameters such as pH, the concentration of Ca²⁺ (C1) (kg/m³), CO₃²⁻ (C2) (kg/m³), and the solubility 

constant (Ksp) (kg²/m⁶) of CaO₃ in water. The model incorporates the chemical reaction rate for crystal formation 

(kr, m²/(kg s)). The mass transfer coefficient β (m/s) is also included. Deposition resistance factor α (Eq(17)), is 

an experimental and dimensionless parameter dependent on viscous and inertial stresses. The thickness 

generated by scaling can be determined to by Eq(18). 

𝛼 =
191

𝑓 ∙  𝑅𝑒1.67
 (17) 

𝑥𝑓 = 𝑅𝑠𝜆𝑓 (18) 

The overall efficiency (ηt) can be evaluated from Eq(19): 

𝜂𝑓 =
�̇�𝑢

𝐼𝐺𝐴𝑠
 (19) 

From Eq(20), the pressure drop within the collector network can be calculated, which is proportional to the sum 

of hydraulic resistances Ki (kPa s²/m⁶) and the square of volumetric flow rate �̇� (m³/s). 

𝛥𝑃𝑇 = �̇�2 ∑ 𝐾

𝑛

𝑖=1

 (20) 

𝐾1 =
8𝐿𝑡

𝜋2𝑑𝑠
5

𝑓 (21) 

𝐾2 =
8𝜌

𝜋2𝑑𝑠
4 𝑘𝑓 (22) 

Eq(21) and Eq(22) illustrate the primary hydraulic resistances. The frictional resistance K1 (kPa s²/m⁶) is due to 

pipe length, and the loss coefficient resistance K2 (kPa s²/m⁶) includes components such as elbows, valves, etc.  

Where f is the friction, kf is the loss coefficient for fittings, Lt (m) and ds (m) are the length and hydraulic diameter 

of the tube. 

3. Thermal model validation 

Experimental data from Gao et al. (2020) were used to validate the model. Figure 2(a) shows the experimental 

data (blue points) and the theoretical results (black line). It is observed that the theoretical results are very close 

to the experimental ones, with a maximum error of 2 % as shown in Figure 2(b). These results demonstrate the 

accuracy of the thermal model. 

 

Figure 2: Comparison of the experimental and simulation results: a) outlet temperature vs. inlet temperature, b) 

error between predicted and measured outlet temperature 

(b) (a) 

120 130 140 150 160 170

120

130

140

150

160

170

Tsim (°C)

T
e
x
p
 (

°C
)

+2%

-2%

(b)

100 110 120 130 140 150 160 170
110

120

130

140

150

160

170

Ti (°C) 

T
o
 (

°C
)

Texp

Tsim

(a)

298



4. Results 

In this study, a solar collector network was designed with the goal of reaching a temperature of 90 °C at 9:00 

a.m. For this calculation, a solar radiation level of 688 W/m² was considered in the city of Zacatecas (Mexico) 

on a typical summer day, with a total flow rate of 80 l/min and an inlet temperature of 25 °C. The number of 

collectors connected in series per line required to achieve the target temperature (90 °C) depends on both the 

total flow rate (80 L/min) of the system and the total number of lines in the network. In this analysis, two network 

configurations were considered: one with 20 lines and another with 16 lines. The flow velocity was 0.12 m/s per 

collector for the first configuration and 0.15 m/s for the s. The operational performance of the plant was analysed 

over 5,040 h. The results showed that significant variations occurred every 720 h (every two months). Figure 2a 

displays the points where these effects were examined. Also, Figure 3a shows that, under initial conditions 

(without fouling), a network of 340 collectors is needed to reach 90 °C with a flow velocity of 0.12 m/s. This 

network was configured with 20 lines and 17 collectors connected in series per line. For a flow velocity of 0.15 

m/s (16 lines), 21 collectors in series per line are required, resulting in a total of 336 collectors.  

 

Figure 3: Thermal performance degradation as fouling builds up over time for different flow velocities: a) Number 

of collectors required, b) Outlet temperature 

As operational time increases, fouling due to scaling inside the solar collectors reduces heat transfer. This 

necessitates increasing the number of collectors required to reach the target temperature. After 5,040 h of 

operation, with a flow velocity of 0.12 m/s, two additional collectors per line are needed, resulting in a total of 

380 collectors in the network. For a flow velocity of 0.15 m/s, one additional collector per line is required after 

the same operation time, bringing the total to 352 collectors. Figure 3b shows the evolution of the outlet 

temperature (To) in the solar collector network as a function of operating time for two flow velocities: 0.12 m/s 

(blue line) and 0.15 m/s (black line). Over time, the temperature progressively decreases, along with a reduction 

in heat transfer and thermal efficiency of the system, all due to fouling caused by scaling. The temperature drop 

is more pronounced at 0.12 m/s, indicating that lower flow velocity promotes deposit accumulation and 

accelerates efficiency loss. After 5,040 h of operation, the outlet temperature significantly decreases in both 

configurations. In the network with a flow velocity of 0.15 m/s, the temperature reduction is 4.28 °C, while at a 

flow velocity of 0.12 m/s, the decrease reaches 5.21 °C. This confirms that higher flow rates help mitigate the 

adverse effects of scaling. Figure 4a presents the thermal efficiency profiles (ηf) of a solar collector network as 

a function of outlet temperature (To) for various operating times, considering the presence of fouling. It is 

observed that in all cases, thermal efficiency decreases as the outlet temperature increases. This is because 

higher temperatures result in increased thermal losses, reducing the system's capacity to transfer heat 

efficiently. The efficiency curve without fouling shows the best performance, while as time progresses (from 720 

h to 5,040 h), the curves shift towards lower efficiency values. This indicates that the accumulation of scaling 

reduces heat transfer capacity, negatively affecting the system performance. The curves in Figure 4b show the 

pressure drop (ΔP) as a function of the number of solar collectors connected in series (Nc) for different operating 

times, considering the presence of fouling. The pressure drops increase as the number of solar collectors 

connected in series rises, due to the greater hydraulic resistance to flow. The pressure drops profiles shown in 

Figure 3b, for up to 10 collectors connected in series, were very similar across different operating times. 

However, for configurations with more than 15 collectors in series, the difference between the pressure drop 

profiles reaches up to 6,000 kPa. 

0 720 1440 2160 2880 3600 4320 5040
16

17

18

19

20

21

22

Operation time (h) 

NC 
0.12 m/s

v=0.15 m/s

Total Flow 80 l/min

250 ppm CaCO3

IG=688 W/m
2

To=90°C

Ti=25°C

(b) (a) 

0 720 1440 2160 2880 3600 4320 5040
87

88

89

90

91

92

93

Operation time (h) 

T
o
  
(°

C
)

0.12 m/s

Total Flow 80 l/min

250 ppm CaCO3

IG=688 W/m
2

Ti=25°C

0.15 m/s

299



 

Figure 4: Performance variation due to fouling accumulation at different stages of operation: a) Efficiency vs. 

Outlet temperature, b) Pressure drop against number of collectors in series 

As operating time increases, the pressure drop increases considerably because of the scaling impact in 

networks with more than 15 collectors arranged in series. The reference curve ("No Fouling") indicates the 

lowest pressure drop, suggesting an unrestricted flow. However, after 2,160 h, the pressure drop reaches 

extremely high values, indicating severe blockage in the ducts caused by the accumulation of deposits. 

5. Conclusions 

The presence of scaling gradually reduces thermal efficiency, necessitating a larger number of collectors to 

maintain the desired outlet temperature. At a flow velocity of 0.15 m/s, 21 collectors in series are required to 

reach the target temperature under clean conditions, whereas with scaling, this number increases to 22. On the 

other hand, at a flow velocity of 0.12 m/s, the system requires 17 collectors under clean conditions, but with 

fouling, it increases to 19. The results reveal that the pressure drop in the solar collector network increases 

significantly, especially when more than 10 collectors are connected in series and operating times exceed 2,160 

h. This affects system performance and can increase pumping costs, highlighting the importance of mitigation 

strategies such as periodic cleaning or water treatment. The water flow velocity within the system directly 

influences the fouling rate: a higher flow velocity (0.15 m/s) helps mitigate its impact, and a lower flow velocity 

(0.12 m/s) accelerates the decrease in outlet temperature. However, it is important to consider that higher flow 

velocity leads to greater pressure drops, which increases pumping costs. Therefore, a network design with 

proper flow distribution not only improves system efficiency but also contributes to reducing operational costs 

and extending its lifespan. 

References 

Albizzati E., 2016, Sustainability assessment of solar installations with flat plate and evacuated tube collectors. 

International Journal of Environmental Pollution, 32, 315-322.  

Bellos E., Tzivanidis C., 2023, A detailed investigation of an evacuated flat plate solar collector. Applied Thermal 

Engineering, 234, 121334.  

Carrión-Chamba W., Murillo-Torres W., Montero-Izquierdo A., 2022, A review of the state-of-the-art of solar 

thermal collectors applied in the industry. INGENIUS, 27, 59-73. 

Gao D., Gao G., Cao J., Zhong S., Ren X., Dabwan Y. N., Hu M., Jiao D., Kwan T. H., Pei G., 2020, Experimental 

and numerical analysis of an efficiently optimized evacuated flat plate solar collector under medium 

temperature. Applied Energy, 269, 115129.  

Haghverdi K., Martinopoulos G., Misirlis D., 2023, Fluid Flow and Heat Transfer CFD Analysis Inside Solar Flat 

Plate Collectors. Chemical Engineering Transactions, 103, 457-462. 

Lugo-Granados H., Picón-Núñez M., 2017, Scaling Growth in Heat Transfer Surfaces and Its Thermohydraulic 

Effect Upon the Performance of Cooling Systems. Chemical Engineering Transactions. 103, 421-426. 

Lugo-Granados H., Canizalez-Dávalos L., Picón-Núñez M., 2023, Thermohydraulic Effects of Scaling in Flat 

Plate Solar Collector Networks. Chemical Engineering Transactions, 103, 421-426.  

Lugo-Granados H.G., Picón-Núñez M., Canizalez-Dávalos L., 2024, Flat plate solar collector networks: Design 

and retrofit considering fouling effects. Thermal Science and Engineering Progress, 51, 102633.  

Nedunchezhiyan M., Ramalingam S., Natesan P., Sampath S., 2025, CFD-Based Optimization of Solar Water 

Heating Systems: Integrating Evacuated Tube and Flat Plate Collectors for Enhanced Efficiency. Case 

Studies in Thermal Engineering, 69, 106017.  

(b) (a) 

30 40 50 60 70 80 90 100
0.5

0.55

0.6

0.65

0.7

0.75

0.8

To  (°C)

hf

 No fouling

720 h

1,440 h

2,160 h

2,880 h2,880 h

3,600 h

4,320 h

Total Flow 80 l/min

250 ppm CaCO3

IG=688 W/m
2

Ti=25°C

5,040 h

v=0.12 m/s

0 2 4 6 8 10 12 14 16 18 20
0

500

1000

1500

2000

2500

3000

3500

4000

Nc 

D
P

 (
k
P

a
)

No Fouling

720 h

1,440 h

2,880 h

2,160 h

3,600 h

4,320 h

5,040 h

Total Flow 80 l/min

250 ppm CaCO3

IG=688 W/m
2

Ti=25°C

v=0.12 m/s

300


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	The Effect of Fluid Velocity on the Performance of Evacuated Solar Thermal Collectors Under Scaling Conditions